Instability of the Cauchy-Kovalevskaya solution for a class of nonlinear systems
Chaojiang Xu
Université de Rouen
We prove that in any smooth-neighborhood of an analytic Cauchy
datum, there exists a smooth function such that the corresponding
initial value problem does not have any classical solution for
a class of first-order non-linear systems. We use a method initiated
by G. M\'etivier for elliptic systems based on the representation
of solutions and on the FBI transform; in our case the system
can be hyperbolic at initial time, but the characteristic roots
leave the real line at positive times.
The results of this talk is obtained in collaboration with
N. Lerner and Y. Morimoto.